HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 9 · 40 questions

How to solve it (Together again or cut equally?): “Ring together again”, “smallest number both divide” → LCM: count in the bigger number until the smaller one divides it. “Longest equal pieces”, “greatest number of identical packs” → HCF: list the factors and pick the greatest common one. Check: the LCM is divisible by both numbers; the HCF divides both numbers.

1. 1.A teacher has 33 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 55 (c) 33 (d) 11
2. 2.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 70 min (c) 140 min (d) 24 min
3. 3.Two ribbons are 12 cm and 21 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 12 cm (c) 1 cm (d) 9 cm
4. 4.A teacher has 44 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 44 (b) 11 (c) 55 (d) 1
5. 5.Two ribbons are 24 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 30 cm (c) 6 cm (d) 24 cm
6. 6.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 15 (d) 18
7. 7.Two ribbons are 56 cm and 63 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 1 cm (b) 504 cm (c) 7 cm (d) 56 cm
8. 8.Two ribbons are 9 cm and 15 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 9 cm (b) 1 cm (c) 3 cm (d) 6 cm
9. 9.Two ribbons are 24 cm and 32 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 24 cm (b) 4 cm (c) 96 cm (d) 8 cm
10. 10.A teacher has 10 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 1 (d) 10
11. 11.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 20 (b) 21 (c) 40 (d) 14
12. 12.Two ribbons are 16 cm and 40 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 8 cm (b) 24 cm (c) 16 cm (d) 4 cm
13. 13.A teacher has 33 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 22 (c) 11 (d) 33
14. 14.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 120 (b) 720 (c) 240 (d) 54
15. 15.Two ribbons are 12 cm and 32 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 4 cm (b) 20 cm (c) 12 cm (d) 2 cm
16. 16.Two ribbons are 21 cm and 27 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 6 cm (b) 21 cm (c) 1 cm (d) 3 cm
17. 17.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 504 min (c) 84 min (d) 6 min
18. 18.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 31 (b) 30 (c) 60 (d) 16
19. 19.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 60 min (c) 30 min (d) 16 min
20. 20.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 21 min (b) 108 min (c) 3 min (d) 36 min
21. 21.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 350 (c) 70 (d) 45
22. 22.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 35 min (b) 250 min (c) 5 min (d) 50 min
23. 23.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 27 min (b) 180 min (c) 3 min (d) 60 min
24. 24.Two ribbons are 18 cm and 63 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 18 cm (b) 3 cm (c) 45 cm (d) 9 cm
25. 25.Two ribbons are 21 cm and 28 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 21 cm (b) 7 cm (c) 84 cm (d) 1 cm
26. 26.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 150 min (b) 25 min (c) 5 min (d) 30 min
27. 27.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 240 (b) 44 (c) 120 (d) 480
28. 28.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 5 min (c) 100 min (d) 500 min
29. 29.Two ribbons are 48 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 432 cm (b) 3 cm (c) 48 cm (d) 6 cm
30. 30.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 140 (c) 280 (d) 700
31. 31.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 84 min (c) 20 min (d) 42 min
32. 32.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 56 (b) 57 (c) 112 (d) 22
33. 33.A teacher has 24 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 12 (c) 6 (d) 84
34. 34.A teacher has 30 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 6 (c) 12 (d) 3
35. 35.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 320 min (b) 4 min (c) 36 min (d) 80 min
36. 36.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 25 (b) 24 (c) 14 (d) 48
37. 37.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 135 min (b) 45 min (c) 24 min (d) 3 min
38. 38.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 180 (b) 27 (c) 120 (d) 60
39. 39.A teacher has 55 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 22 (b) 11 (c) 1 (d) 55
40. 40.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 41 (b) 40 (c) 18 (d) 80

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